MathDB

3

Part of 2019 India National OIympiad

Problems(1)

INMO 2019 P3

Source:

1/20/2019
Let m,nm,n be distinct positive integers. Prove that gcd(m,n)+gcd(m+1,n+1)+gcd(m+2,n+2)≤2∣m−n∣+1.gcd(m,n) + gcd(m+1,n+1) + gcd(m+2,n+2) \le 2|m-n| + 1. Further, determine when equality holds.
number theory